Hi Bamitz,
Welcome to the Apple Support Communities!
I understand that when you sync your iPhone to your computer, some songs don’t appear to be playable on the device. We know that syncing issues can be very frustrating, but we are here to help!
Before we begin troubleshooting, I would make sure that all of your purchased content from iTunes is located in your iTunes library. Use the following article to make sure all of your past purchases have been downloaded.
Download your past purchases - Apple Support
Once all of your music is in your iTunes library and is playing as expected, we’ll begin troubleshooting the sync issue.
To begin troubleshooting, I would suggest removing all music from your iPhone completely using iTunes. This will give us a blank slate to work with so we can sync your content back to your iPod fresh.
1. Connect your iPhone to iTunes and select it
2. Select Music under Settings in the left hand side of iTunes
3. Remove the check from Sync Music (You will get a warning that all music will be removed. You are okay to proceed)
4. Select Apply in the lower right corner of iTunes to apply the changes
5. After the sync finishes, verify on your iPhone that all music has been removed
Once all of the music has been removed from the iPhone, we’ll go back through the syncing process to move your music and playlists back to the iPod.
1. You are probably still on the Music pane in iTunes, but if not, follow steps 1-2 in the previous instructions to return
2. Check the box next to Sync Music and make your selections for music and playlists that you would like added to your iPod
3. Select Apply in the lower right corner of iTunes to apply the changes
Sync your iPhone, iPad, or iPod touch with iTunes using USB - Apple Support
If you are still experiencing a content issue on your iPhone after syncing, please let us know in further detail about your situation so we can provide continued support.
Cheers!